When Duryodhana was born several bad omens were noticed around the palace. Wise men, including Vidura said that the boy must be discarded quoting the following verse :
"Tyaje-dekam kulasyaarthe graamasyaarthe kulam tyajed
Graamam janapadasyaarthe aatmarthe prithiveem tyajed"
May one person be sacrificed for the sake of the family, a family for the sake of a village and a village to save an entire nation. Yet, the entire earth may be sacrificed to save oneself.
Here it is the interest of the kingdom of Kurus was at stake. Hence, Duryodhana, whose birth caused ill portents must be sacrificed . The last clause is applicable from the point of view of an individual in danger.